Pseudo-Goldstone bosons in curved space-time

We calculate the effective potential for pseudo-Goldstone bosons (PGBs) in a toy SU(3) gauge theory broken by scalars in the adjoint representation, in the Einstein static universe R1×S3 with constant scalar curvature R. In both the strong- and weak-gravitational-field limits, the effective potential for the PGBs picks up curvature-dependent quadratic terms in one-loop order. Curiously, in the weak-field limit, the gravitational contribution to the PGB mass is of the form R lnR, while in the opposite case (strong field) the expected form linear in R is recovered. A subtlety involved in determining the coupling of Goldstone bosons to the scalar curvature in theories with spontaneous symmetry breaking is described.